Indicial representation of higher order optimal controls for a Duffing oscillator

The Duffing oscillator is a useful model for the uncontrolled behavior of structural systems including columns, gyroscopes, plates and certain types of bridges. A study is made of a class of nonlinear optimal controls for these oscillators, and the effects of higher order feedback corrections based on series expansions of the optimal cost function and the optimal control function in a Hamilton-Jacobi context are determined. A novel representation of the solution is presented, in terms of the indicial formulation of tensor algebra. For the case in point, the indicial approach offers a conceptually attractive alternative to the general tensor solutions. Numerical studies and an analysis of the effect of higher order feedbacks on the nonzero equilibrium points of the controlled system are presented